Fluid antenna systems (FASs) have shown that activating a single port from a densely packed antenna array can yield spatial diversity comparable to that of tens of independent antennas, a property that has substantially improved communication reliability and efficiency. The fluid antenna array (FAA) extends this concept to multi-port configurations while avoiding complex multi-dimensional spatial correlation, and offers significant geometrical flexibility under a finite aperture and a limited port budget. These attributes motivate environment-adaptive array geometry for sensing in integrated sensing and communication (ISAC) systems. Although this flexibility enables adaptive array geometries that exploit near-field distance-angle information, improving multi-parameter target estimation under communication and deployment constraints remains challenging. In this paper, we propose a planar FAA-assisted near-field ISAC framework for multiuser communication and target sensing. Specifically, we derive the Fisher information matrix (FIM) and the corresponding Cramér-Rao bound (CRB) for the joint estimation of target range, zenith angle, azimuth angle, and radial velocity. Based on the derived CRB, we jointly optimize the FAA port positions and transmit beamforming to improve sensing accuracy while satisfying communication signal-to-interference-plus-noise ratio (SINR), transmit power, and physical deployment constraints. To solve the resulting non-convex problem, we develop a two-stage alternating optimization algorithm, in which transmit beamforming is optimized through semidefinite relaxation (SDR), while FAA port positions are successively optimized through discrete search and continuous refinement. Simulation results indicate that the proposed algorithm achieves favorable sensing performance while maintaining a reasonable computational cost.

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